Seismic Design Forces on Submerged Components in Sloshing Zone

[supratikbose1989]

Hi Everyone,

I am looking for some references in the literature that talks about the seismic design forces to be considered for submerged structural (columns at the center of the tank supporting the tank roof) or nonstructural (baffler in wastewater clarifier, etc.) components that are present in the sloshing zone of the liquid.

Any help will be appreciated.

Regards,
Supratik

 

[phamENG]

I don't know of any specific references, but I do have an idea for something you could look for: wave tank designs. That's essentially what you have. A wave tank has a movable wall that oscillates back and forth to generate waves. In an earthquake, the wall of your tank will behave in a similar fashion. If you have the expected period and acceleration of your design earthquake, you should be able to use wave tank principles to predict at least the initial wave action in your tank. Accounted for rounded walls and the effects of wave reflection will be challenging, though. But at least for the initial phase, you can predict the waves you'll have and use traditional wave force techniques to estimate the load. You just have to make some judgments about how the movement of the tank and columns within it will vary with time compared to the velocity of the waves. An interesting problem.

 

[WARose]

The main references that comes to my mind are: 'Design of Liquid-Containing Concrete Structures for Earthquake Forces', by: Munshi. (Published by PCA.)

I've got the (original) 2002 version. I don't know if they've updated it since.

Also, ACI 350.3 comes to mind.

For the load on your column, you'd probably wind up using something similar to the wall load (for sloshing).

 

[JStephen]

There's an old technical paper by Wozniak, "The Basis of Seismic Design for API-650" or something of the sort. In an appendix of that paper, he gives a formula and derivation for this. It's in terms of the UBC zone factors, etc., so you have to work out the equivalent terms for the latest API/ASCE approaches.

 

[supratikbose1989]

Thank you everyone for the help. I was going through the 'Design of Liquid-Containing Concrete Structures for Earthquake Forces', by: Munshi as recommended by WARose, I figured out I need to consider an added mass in the submerged elements to account for the impulsive component and drag forces to consider the effect of the sloshing of the liquid. However, the drag force is a function of the horizontal sloshing velocity. Please let me know, how I can calculate the horizontal sloshing velocity.

 

[WARose]

I was going through the 'Design of Liquid-Containing Concrete Structures for Earthquake Forces', by: Munshi as recommended by WARose, I figured out I need to consider an added mass in the submerged elements to account for the impulsive component and drag forces to consider the effect of the sloshing of the liquid. However, the drag force is a function of the horizontal sloshing velocity. Please let me know, how I can calculate the horizontal sloshing velocity.

The cited source gives the sloshing period [T[sub]c[/sub] on p.17], from that (and the wave height; also given in the text) you should be able to figure the velocity.

 

[supratikbose1989]

Thank you WARose. I am not still sure how to calculate the sloshing velocity.Can I use the response spectra and the convective period (Tc) to determine the sloshing velocity?

 

[supratikbose1989]

Thank you JStephen for your response. But I could not access the paper, do you have it?

 

[WARose]

Thank you WARose. I am not still sure how to calculate the sloshing velocity.Can I use the response spectra and the convective period (Tc) to determine the sloshing velocity?

It's a wave mechanics problem. And it depends on: is it in deep or shallow water? The deep water solution is pretty straight forward and you could figure it based on the wave period [T[sub]c[/sub]] and wave height. If you have 'Structural Dynamics: Theory and Applications' (by Tedesco), Chapter 20 is a good resource for water waves.

[red]EDIT[/red]: Found another good resource here:

https://en.wikipedia.org/wiki/Wind_wave#Spectrum

 

[JStephen]

I've got a copy at the office, don't have it here at the house.